Measurement optimization of variational quantum simulation by classical shadow and derandomization

TL;DR

This paper proposes a novel measurement optimization algorithm for variational quantum simulation (VQS) using classical shadow and derandomization techniques, significantly reducing measurement costs for large quantum systems.

Contribution

It introduces a new method to apply shadow-based measurement strategies to VQS, bridging the gap from VQO and providing theoretical and numerical validation.

Findings

The algorithm reduces measurement requirements in VQS.

Theoretical analysis confirms the advantage of the method.

Numerical experiments validate effectiveness on quantum chemical systems.

Abstract

Simulating large quantum systems is the ultimate goal of quantum computing. Variational quantum simulation (VQS) gives us a tool to achieve the goal in near-term devices by distributing the computation load to both classical and quantum computers. However, as the size of the quantum system becomes large, the execution of VQS becomes more and more challenging. One of the most severe challenges is the drastic increase in the number of measurements; for example, the number of measurements tends to increase by the fourth power of the number of qubits in a quantum simulation with a chemical Hamiltonian. This work aims to dramatically decrease the number of measurements in VQS by recently proposed shadow-based strategies such as classical shadow and derandomization. Even though previous literature shows that shadow-based strategies successfully optimize measurements in the variational quantum optimization (VQO), how to apply them to VQS was unclear due to the gap between VQO and VQS in measuring observables. In this paper, we bridge the gap by changing the way of measuring observables in VQS and propose an algorithm to optimize measurements in VQS by shadow-based strategies. Our theoretical analysis not only reveals the advantage of using our algorithm in VQS but theoretically supports using shadow-based strategies in VQO, whose advantage has only been given numerically. Additionally, our numerical experiment shows the validity of using our algorithm with a quantum chemical system.